What is the distance from the point (1, 2) to the line x + y = 5? (2020)

What is the distance from the point (1, 2) to the line x + y = 5? (2020)

Step 1: Identify the point and the line. The point is (1, 2) and the line is given by the equation x + y = 5.
Step 2: Rewrite the line equation in the form Ax + By + C = 0. The line x + y = 5 can be rewritten as x + y - 5 = 0, where A = 1, B = 1, and C = -5.
Step 3: Use the distance formula from a point (x0, y0) to a line Ax + By + C = 0. The formula is Distance = |Ax0 + By0 + C| / √(A² + B²).
Step 4: Substitute the values into the formula. Here, (x0, y0) = (1, 2), A = 1, B = 1, and C = -5.
Step 5: Calculate the numerator: |1*1 + 1*2 - 5| = |1 + 2 - 5| = |-2| = 2.
Step 6: Calculate the denominator: √(1² + 1²) = √(1 + 1) = √2.
Step 7: Divide the numerator by the denominator: Distance = 2 / √2.
Step 8: Simplify the distance: 2 / √2 = √2.

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